Question

07. Find six consecutive integers that are composites and find the smallest such string.​

Answer 1

Answer:

90 , 91 , 92 , 93 , 94 , 95

Step-by-step explanation:

Any Six Consecutive inetegrs Would Have atleast  

3 Even Numbers

Atleast have a numbers multiples of 3  other than 3  even  numbers

so one remaining number need to be Composite

we can call six such numbers

6k , 6k+1 , 6k+2 , 6k+3 , 6k+4 , 6k+5

we Just need to check that

6k + 1  & 6k+5 are composite

k = 4   will give 25 & 29  but 29 is Prime

k  =8  Will given 49 & 53  but 53 is prime

k  =9  will give 55 & 59  but 59 is prime

k = 14  will give 84 & 89  but 89 is prime

k = 15  will give 91  & 95  both are composites

90 , 91 , 92 , 93 , 94 , 95

are consecutive integers which are Prime